Assume an individual has 20 birr to spend on two products: X1 and X2 each with market price of 2(two) birr. If the total utility the consumer generates from the two products is as given on the table below,
1.1= Select all combinations of X1 and X2 that fulfill the necessary conditions of consumer equilibrium, and from them identify the consumer’s equilibrium purchase size
Q =1 2 3 4 5 6 7 8 9 10 11
TUX1 =16 30 41 51 60 68 75 81 86 89 90
TUX2 =15 28 40 48 54 59 63 66 68 69 69
A. Combinations of X1 and X2 that fulfill the necessary conditions of consumer equilibrium: (X1=10, X2=10), (X1=9, X2=11), (X1=8, X2=12), (X1=7, X2=13), (X1=6, X2=14), (X1=5, X2=15).
B. Consumer’s equilibrium purchase size: (X1=10, X2=10).
To find the consumer's equilibrium purchase size, we need to identify the combination of X1 and X2 that maximizes the total utility (TUX1 + TUX2) while considering the budget constraint.
The budget constraint states that the consumer has 20 birr to spend, and each product (X1 and X2) has a market price of 2 birr. This means that the consumer can buy a maximum of 10 units of each product (20 birr / 2 birr per unit).
To determine the equilibrium purchase size, we can compare the total utility generated from each combination of X1 and X2 and select the combinations that fulfill the necessary conditions:
Combination: (Q=1, TUX1=16, TUX2=15)
Utility: TUX1 + TUX2 = 16 + 15 = 31
Combination: (Q=2, TUX1=30, TUX2=28)
Utility: TUX1 + TUX2 = 30 + 28 = 58
Combination: (Q=3, TUX1=41, TUX2=40)
Utility: TUX1 + TUX2 = 41 + 40 = 81
Combination: (Q=4, TUX1=51, TUX2=48)
Utility: TUX1 + TUX2 = 51 + 48 = 99
Combination: (Q=5, TUX1=60, TUX2=54)
Utility: TUX1 + TUX2 = 60 + 54 = 114
Combination: (Q=6, TUX1=68, TUX2=59)
Utility: TUX1 + TUX2 = 68 + 59 = 127
Combination: (Q=7, TUX1=75, TUX2=63)
Utility: TUX1 + TUX2 = 75 + 63 = 138
Combination: (Q=8, TUX1=81, TUX2=66)
Utility: TUX1 + TUX2 = 81 + 66 = 147
Combination: (Q=9, TUX1=86, TUX2=68)
Utility: TUX1 + TUX2 = 86 + 68 = 154
Combination: (Q=10, TUX1=89, TUX2=69)
Utility: TUX1 + TUX2 = 89 + 69 = 158
Combination: (Q=11, TUX1=90, TUX2=69)
Utility: TUX1 + TUX2 = 90 + 69 = 159
From the above combinations, the consumer's equilibrium purchase size is determined by the combination that provides the highest total utility while not exceeding the budget constraint. In this case, the combination with the highest utility and within the budget is:
Combination: (Q=10, TUX1=89, TUX2=69)
Utility: TUX1 + TUX2 = 89 + 69 = 158
Therefore, the consumer's equilibrium purchase size is 10 units of X1 and 10 units of X2.
To identify the consumer's equilibrium purchase size, we need to select combinations of X1 and X2 that fulfill the necessary conditions of consumer equilibrium. In this case, consumer equilibrium occurs when the consumer maximizes their utility given their budget constraint.
The consumer's budget constraint is that they have 20 birr to spend on two products with a market price of 2 birr each. So the consumer can purchase a maximum of 10 units of each product (since 20 birr divided by 2 birr per unit equals 10 units).
To identify the consumer's equilibrium purchase size, we need to find combinations of X1 and X2 that maximize total utility (TUX1 + TUX2), while not exceeding the budget constraint of 20 birr.
Looking at the table, here are the combinations of X1 and X2 that fulfill the necessary conditions of consumer equilibrium and their corresponding total utilities:
Combination 1: Q(X1) = 11, Q(X2) = 0 (Total Utility = TUX1 = 90)
Combination 2: Q(X1) = 10, Q(X2) = 1 (Total Utility = TUX1 + TUX2 = 89 + 69 = 158)
Combination 3: Q(X1) = 9, Q(X2) = 2 (Total Utility = TUX1 + TUX2 = 86 + 68 = 154)
Combination 4: Q(X1) = 8, Q(X2) = 3 (Total Utility = TUX1 + TUX2 = 81 + 63 = 144)
Combination 5: Q(X1) = 7, Q(X2) = 4 (Total Utility = TUX1 + TUX2 = 75 + 59 = 134)
Combination 6: Q(X1) = 6, Q(X2) = 5 (Total Utility = TUX1 + TUX2 = 68 + 54 = 122)
From these combinations, the consumer's equilibrium purchase size would be Combination 1, where they would purchase 11 units of X1 and 0 units of X2. This combination maximizes their total utility (90) and does not exceed their budget constraint.